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9

Detection of Earth-impacting asteroids

with the next generation all-sky surveys

Peter Veres1, Robert Jedicke2, Richard Wainscoat2, Mikael Granvik2,

Steve Chesley3, Shinsuke Abe4, Larry Denneau2, Tommy Grav5,

ABSTRACT

We have performed a simulation of a next generation sky survey’s (Pan-

STARRS 1) efficiency for detecting Earth-impacting asteroids. The steady-state

sky-plane distribution of the impactors long before impact is concentrated to-

wards small solar elongations (Chesley & Spahr 2004) but we find that there is

interesting and potentially exploitable behavior in the sky-plane distribution in

the months leading up to impact. The next generation surveys will find most

of the dangerous impactors (>140 m diameter) during their decade-long survey

missions though there is the potential to miss difficult objects with long synodic

periods appearing in the direction of the Sun, as well as objects with long orbital

periods that spend much of their time far from the Sun and Earth. A space-based

platform that can observe close to the Sun may be needed to identify many of

the potential impactors that spend much of their time interior to the Earth’s

orbit. The next generation surveys have a good chance of imaging a bolide like

2008 TC3 before it enters the atmosphere but the difficulty will lie in obtaining

enough images in advance of impact to allow an accurate pre-impact orbit to be

computed.

Subject headings: Pan-STARRS; Asteroids; Near-Earth Objects; Meteors; Im-

pact Processes

1Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska Dolina, 842 48

Bratislava, Slovakia

2University of Hawaii, Institute for Astronomy, 2680 Woodlawn Drive, Honolulu, HI 96822-1897, USA

3Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA

4Institute of Astronomy, National Central University, No. 300, Jhongda Rd, Jhongli City, Taoyuan

County 320, Taiwan

5Department of Physics and Astronomy, Bloomberg 243, Johns Hopkins University, 3400 N. Charles St.,

Baltimore, MD, 21218-2686, USA

– 2 –

1. Introduction

Throughout most of human history it was not understood that the Earth has been

battered by large asteroids and comets and that the impacts and subsequent environmental

changes have serious consequences for the survival and evolution of life on the planet. But

in the past ∼50 years more than 170 impact structures have been identified on the surface

of the Earth (Earth-impact database 2008). Were it not for the Earth’s protective atmo-

sphere, oceans, erosion and plate tectonics, the surface of the Earth would be saturated with

impact craters like most other atmosphereless solid bodies in our solar system. While the

impact probability is now relatively well understood as a function of the impactor size (e.g.

Brown et al. 2002; Harris 2007) this work addresses specific questions related to discover-

ing impacting asteroids before they hit the Earth. In particular, we build upon the work

of Chesley & Spahr (2004) and determine the sky-plane distribution of impacting asteroids

before impact and the effectiveness of the next generation large synoptic sky surveys at

identifying impactors.

The first surveys to target near-Earth objects (NEO) (Helin & Shoemaker 1979), as-

teroids and comets with perihelion < 1.3 AU, provided the first look at their orbit and

size distribution and allowed the first determination of the impact rate from NEO statistics

(Shoemaker 1983) rather than crater counting on the Moon. These pioneers heightened the

awareness of the impact risk and gave rise to the current generation of CCD-based aster-

oid and comet surveys such as Spacewatch (Gehrels 1986), LINEAR (Stokes et al. 2000),

LONEOS (Koehn & Bowell 1999), NEAT (Pravdo et al. 1999), and the current leader in

discovering NEOs, the Catalina Sky Survey (CSS) (Larson et al. 1998). These programs

benefitted from the elevated impact risk perception when in 1998 the U.S. Congress followed

the recommendations of Morrison (1992) and mandated that the U.S. National Aeronautics

and Space Administration (NASA) search, find and catalog ≥ 90% of NEOs with diameters

larger than 1 km within 10 years. That goal will probably be achieved within the next few

years. The residual impact risk is mainly due to the remaining undiscovered large aster-

oids and comets (Harris 2007) but Stokes et al. (2004) suggest that the search should be

expanded to identify ≥ 90% of potentially hazardous objects (PHO) by 2020. 1

Stokes et al. (2004) showed that the extended goal cannot be achieved in a reasonable

time frame with existing survey technology. The search needs to be done from space (rapid

completion but at high risk and high cost) or from new ground-based facilities (slower com-

pletion but lower risk and lower cost). Their recommendation dovetailed nicely with the

1A PHO is an object with absolute magnitude H ≤ 22 (∼ 140 m diameter) on an orbit that comes within

0.05 AU of the Earth’s orbit.

– 3 –

Astronomy and Astrophysics Survey Committee (2001) Decadal Report that made a strong

case for the development of a large synoptic survey telescope (LSST) that would provide

the necessary depth and sky coverage to identify the smaller PHOs while also satisfying the

goals of other fields of astronomy.

There are currently a few candidates for a large synoptic survey telescope. The most

ambitious is an 8.4 m system being designed by the eponymous LSSTC (the LSST Corpora-

tion) that anticipates beginning survey operations in 2016 in Chile. With a ∼9 deg2 field of

view and 15 s exposures, simulations suggest that their system could identify &90% of PHOs

in 15 years (Ivezic et al. 2007). A more modest LSST known as the Panoramic Survey Tele-

scope and Rapid Response System (Pan-STARRS) will be composed of four 1.8m telescopes

(PS4) and is expected to be located atop Mauna Kea in Hawaii. A prototype single telescope

for Pan-STARRS known as PS1 should begin operations in mid-2009 from Haleakala, Maui.

With a ∼7 deg2 field of view, the excellent seeing from the summit of Mauna Kea, and the

use of orthogonal transfer array CCDs (Burke et al. 2007) for on-chip image motion com-

pensation, the Pan-STARRS system will be competitive with and completed earlier than the

LSSTC’s system.

The next generation survey telescopes have the potential to be prolific discoverers of

PHOs but Earthlings aren’t so much concerned with statistical impact risk calculated from

PHO orbital distributions as they are interested in whether an impact event will occur. The

statistical risk of a house burning down may seem inconsequential until you consider the

actuality of your house being incinerated. Similarly, while Harris (2008) has calculated that

expected fatalities due to an unanticipated asteroid impact have dropped from ∼1,100/year

before the onset of modern NEO surveys to only ∼80/year now, as a species we would like

to know whether one of the fatality inducing impacts will take place this century. Thus,

this work concentrates on the detection of objects that may impact the Earth in the next

hundred years.

Following Chesley & Spahr (2004) we concentrate on the subset of PHOs that are in

fact destined for a collision with the Earth. They showed that long before impact the im-

pactors’ steady state sky-plane distribution is concentrated on the ecliptic and at small solar

elongation. We extend their analysis and find that the sky-plane distribution of impactors

has interesting and potentially useful structure in the time leading to collision. We also

study the capabilities of one next-generation survey (PS1) at identifying the impactors well

before collision. In particular, we will answer the following questions: How different are

the orbital characteristics of the impactor population and current NEO and PHO models?

What is the survey efficiency for identifying asteroids on a collision course with the Earth as

a function of their diameter? How much warning time will be provided before the impact?

– 4 –

How accurate is the orbital solution prior to impact? How does the MOID2 evolve in time

and is the current definition of a PHO consistent with flagging dangerous objects? What are

the orbital properties of objects that are not found? Are there methods to improve the effi-

ciency of identifying impactors? Given the size-frequency distribution of NEOs what is the

probability that PS1 will actually identify an impactor and what will be its most probable

size?

2. Synthetic Earth-impacting asteroids

Our synthetic impactor population model is described in detail in Chesley & Spahr

(2004) and Grav et al. (2009). Here we provide a brief summary of the technique.

We created∼130,000 impactors based on the NEO population developed by Bottke et al.

(2000) and Bottke et al. (2002) hereafter referred to as the Bottke NEO Model. The model

incorporates objects from both asteroidal and cometary source regions but has at least two

problems that affect its utility for creating an impactor population: 1) it assumes that the

orbit distribution of NEOs is independent of their diameter and 2) it provides the (a, e, i, H)

(semi-major axis, eccentricity, inclination, and absolute magnitude) distribution for NEOs

on a coarse grid that is not suited to the narrower range of orbital elements of the impacting

asteroids. However, there are few options to use as starting points for developing an impactor

population and we will compare our impactor population’s orbit distribution to the known

small impactor population to understand the limitations of our technique.

To generate the impactors NEOs were randomly selected from the Bottke NEO model

and assigned random longitudes of ascending node and arguments of perihelion. Orbits with

a MOID small enough to permit an impact were saved as potential impactors and then filtered

according to their likelihood of impact to obtain the final set of impactors. The likelihood

is the fraction of time that an object spends in close proximity to the Earth’s orbit. i.e.

orbits with a small velocity relative to the Earth tend to have shorter impact intervals and

higher intrinsic impact probabilities. Higher likelihoods received higher weighting in the

selection. If an orbit was chosen as an impactor then a year of impact was randomly selected

between 2010 and 2110 — the date of collision is already randomly fixed by the longitude of

the node at impact. To this point, the process assumed a two-body asteroid orbit with no

planetary perturbations. The final step was to ensure an impact under the influence of all the

perturbations in a complete solar system dynamical model. This was done by differentially

adjusting the two-body argument of perihelion (ω) and orbital anomaly to reach a randomly

2Minimum Orbital Intersection Distance

– 5 –

selected target plane coordinate on the figure of the Earth. The final result is an osculating

element set that leads to an Earth impact when propagated with the full dynamical model.

The full set of impactors generate about three impacts per day uniformly distributed over

the globe with an average separation of about 70 km.3

This technique preferentially selects objects on Earth-like orbits out of the Bottke NEO

model but Brasser & Wiegert (2008) show that objects do not remain long in these types of

orbits. This is not a problem except in the sense addressed above — that the Bottke NEO

model is provided on a relatively coarse grid — because the NEO model already accounts

for NEO ‘residence times’ on all types of NEO orbits. However, since we assume a flat

distribution of NEO orbit elements within the (a, e, i) bin corresponding to Earth-like orbits

it is likely that we generate fractionally more of the extremely Earth-like orbits than exist

in reality.

As shown by Chesley & Spahr (2004) and in Fig. 1 there are important differences

between the impactor population and the NEOs. The impactors have orbits with lower

semi-major axis, inclination and eccentricity. This has the effect of decreasing the Earth

encounter and impact velocity (v∞ and vimp respectively) for the impactors relative to the

NEOs. The decreased impact velocity has implications for modelling the impact crater size-

frequency distribution on the Earth and Moon since lower impact energies per unit mass

require larger impactors to create equivalent-size craters.

As mentioned above, the Bottke NEO model assumed that the orbit distribution of the

NEOs is independent of size. While this assumption is probably fine for large objects it

must break down at smaller sizes due to the effect of non-gravitational forces such as the

Yarkovsky effect (e.g. Bottke et al. 1998; O’Brien & Greenberg 2005). Where the transition

occurs is not clear but Fig. 1 compares the (a, e, i) distribution of our impactor population

to sporadic fireballs from the IAU Meteor Database of photographic orbits (Lindblad et al.

2003). We removed fireballs due to 17 major meteor showers4 (Jenniskens 2006) by requiring

that the meteors not be associated with the parent meteor body using the dimensionless orbit

3Gallant et al. (2006) use a superior (but much more time consuming) technique to generate an even

more unbiased impactor population from the Bottke NEO model and confirm that the latitude and longitude

distribution of impact locations is flat to within a few percent when averaged over all impactors and times

of year.

4From the IAU Meteor Database: Quadrantids, Lyrids, Pi Puppids, Eta Aquarids, Arietids, Daytime

Zeta Perseids, June Bootids, Southern Delta Aquarids, Perseids, Draconids, Orionids, Southern Taurids,

Northern Taurids, Leonids, Puppid/Velids, Geminids, Ursids.

– 6 –

similarity D-criterion of Valsecchi et al. (1999)5:

D2 = [U2 − U1]2 + w1[cos θ2 − cos θ1]

2 +∆ξ2, (1)

where

cos θ =1− U2 − 1/a

2U,

∆ξ2 = min[ w2∆φ2

A + w3∆λ2

⊕A, w2∆φ2

B + w3∆λ2

⊕B ],

φA = 2 sin(φ2 − φ1

2

)

,

φB = 2 sin(π + φ2 − φ1

2

)

,

λ⊕A = 2 sin(λ⊕2 − λ⊕1

2

)

,

λ⊕B = 2 sin(π + λ⊕2 − λ⊕1

2

)

.

The 1 and 2 subscripts refer to the two bodies whose orbits are being compared, U is the

unperturbed geocentric speed just prior to impact, (θ, φ) define the direction of the radiant in

a frame moving with the Earth about the Sun, and λ⊕ is the ecliptic longitude of the Earth at

the time of meteoroid impact. The weighting factors wi were set to 1 as per Valsecchi et al.

(1999). All objects with D-criterion relative to a parent body of ≤ 0.2 were discarded (577

meteors) leaving 2002 sporadic background fireballs.

The impactor and NEO orbit distributions have already been discussed briefly above

and in detail by Chesley & Spahr (2004). The differences between the impactor population

and the fireballs are perhaps more interesting where it is important to keep in mind that

the comparison in Fig. 1 is between the bias corrected impactor population and the ob-

served bolide population. We believe that the apparent difference between the impactor and

bolide distributions is a consequence of the uncorrected observational selection effects in the

bolide data along with modifications in the distributions due to the Yarkovsky effect (e.g.

Farinella et al. 1998). The bolide detection technique has a strong bias towards high kinetic

energy events that preferentially detects objects on cometary-like orbits (Ceplecha et al.

1998). Indeed, if we consider ‘comets’ to be objects from our sporadic bolide data with

a > 4 AU or e > 0.9 or i > 90 then ∼13.4% of the objects are of ‘cometary’ origin. This

value is about twice the cometary fraction of 6 ± 4% suggested by the Bottke NEO model

and consistent with the expected ‘comet’ enhancement in the bolide data. On the other

hand, it is only half the 25% cometary contribution suggested by Stuart & Binzel (2004).

5We obtain essentially identical results using otherD-criterion formulations (Southworth & Hawkins 1963;

Drummond 1981; Galligan 2001) with corresponding but different upper limits on the D-criterion value.

– 7 –

No meteor or fireball had ever been detected before entering the Earth’s atmosphere

before we generated our synthetic population of Earth-impacting asteroids6. Then, on 7 Oc-

tober 2008, asteroid 2008 TC3 was discovered by CSS using their 1.5 m telescope. Rapid fol-

lowup by other observatories made it almost immediately clear that the few-meter-diameter

(H = 30.7) asteroid would enter the Earth’s atmosphere within a day and explode over

northern Sudan. The substantial and largely self-organized follow-up effort resulted in 789

astrometric observations from amateur and professional observatories worldwide being sub-

mitted to the Minor Planet Center. Due to the parallax induced by the distance between

the observatories and the proximity of the asteroid, the observations allowed an accurate

pre-impact orbit to be computed despite the short observational timespan (Table 1). The

pre-impact orbit is very consistent with our predicted impactor orbit distribution as shown

in Fig. 1. Note that, in particular for the eccentricity, the pre-impact orbit matches the

expected impactor population better than the debiased NEO population or the observed

bolide population.

Orbital elements and their uncertainties for 2008 TC3

a [AU] e i [] Ω [] ω [] M0 []

Elements 1.2712175 0.2856863 2.331633 194.1308964 233.954719 328.58963

1-σ unc 0.0000031 0.0000023 0.000017 0.0000011 0.000040 0.00015

Table 1: Keplerian elements and their 1-σ uncertainties for 2008 TC3 for the epoch 2008 Oct

6.11535 TT, about one day before atmospheric entry on 2008 Oct 7.1146 UTC. The orbital

solution made use of 574 astrometric observations (42 of which were discarded as outliers) and

assumed an uncorrelated astrometric uncertainty of 0.5 arcseconds for every measurement.

The orbital solution was obtained using the OpenOrb software (Granvik et al. 2008).

2.1. Time evolution of the impactor population’s MOIDs

Recall that a PHO is defined as an object with H ≤ 22 and a MOID < 0.05 AU with

respect to the Earth’s orbit. We investigated the evolution of the MOID for our impactor

population as a function of time before impact as shown in Fig. 2. All the impactors’s

osculating orbits were integrated using the JPL’s N-body integrator incorporating the effects

of the Sun, eight planets, and the dwarf planets Pluto, Ceres, Vesta and Pallas. MOIDs

were then calculated at different times before impact using the synthetic objects’s integrated

6There were suspected radar detections of exoatmospheric meteoroids in the late 1970’s (Kessler et al.

1980)

– 8 –

osculating orbits at the time of interest, not the orbit derived from synthetic observations

of the object. We see that as the time of impact approaches the MOID decreases such that

one month before impact essentially all objects have a MOID less than the Earth’s capture

radius (b):

b = R ·

√

1 +v2ev2∞

, (2)

where ve represents the escape velocity from the surface of the Earth. Fig. 3 shows that

∼99% of all impactors are identified as PHOs 45 years in advance of impact. Even 100 years

before impact ∼98% of the objects have a MOID<0.05 AU though the fraction of non-PHO

impactors is increasing rapidly as the time before impact increases.

There are a few objects with MOID>0.05 AU that would not be identified as impactors

or PHOs using a single MOID determination from a derived osculating orbit at the time

of discovery. These objects suffer from a close approach to Jupiter that converts them

from a harmless object into an Earth-impactor. Modern impact monitoring sites such as

JPL (Milani et al. 2005) and NEODyS (Chesley & Milani 1999) integrate the orbits of all

objects to identify these unusual but dangerous cases.

At all eight times before impact the cumulative fractional distribution of MOIDs (fC)

in Figs. 2 exhibit a nearly constant slope for fC . 0.9. Under the simple assumption that

the impactors are randomly distributed on the impact plane at the Earth we would expect

fC ∝ MOID2. Thus, we fit the distribution to log fC = log f ′

C +m log[MOID/(10−4AU)]

where f ′

C is (roughly) the cumulative fraction of objects with MOID < 10−4 AU. We find

an average slope over all impact times of m = 0.88 ± 0.01, much less than 2 and quite

different from the result of Tancredi (1998) who found a slope of ∼1.23 for clones of the

extremely Earth orbit-like 1991 VG. We believe that the difference between the expected

quadratic and our measured unit slope is due to the Earth’s gravitational focussing. The

cumulative fraction of impactors with MOID< 10−4 AU as a function of time is shown in

Fig 4a. Clearly, the interpration of fC as a cumulative fraction breaks down for fC & 1 but

we see that essentially all the impactors have MOID< 10−4 AU about 73 days before impact.

Fig 4b provides a quantitative assessment of the time evolution of the mode of the MOID

distribution from Fig. 2. The combination of the fits to the data in Figures 4 allow a rough

determination of the time evolution of the fraction of impactors with a given MOID.

2.2. Sky-plane distribution of Earth-impacting asteroids

In this section we analyze the sky-plane distribution of Earth-impacting asteroids in

the years, months, and days leading up to impact. The topocentric location and brightness

– 9 –

of the impactors (as seen from Mauna Kea in all cases) was calculated for a ∼10K subset

of impactors for every day in the 100 years leading to impact using the OpenOrb software

package (Granvik et al. 2008).

The steady-state7 sky plane distribution of Earth-impactors in Figure 5a shows all ob-

jects that would be visible to PS1 with V < 22.7 assuming that H = 20 (diameter ∼350 m).

The figure clearly shows the high sky-plane density ‘sweet spots’ at small solar elongations

(± ∼ 90) identified by Chesley & Spahr (2004). The objects in the sweet spots are close to

the Earth and therefore relatively bright despite their large phase angles, but are too close

to the Sun to be easily observed.

Twenty years before impact 962 objects (∼9.6%) lie within the sweet spot region that

encompasses topocentric solar elongations from 60 to 90. Of these, 552 (∼5.5%) have an

ecliptic latitude (β) in the range −10 ≤ β ≤ +10 and 826 (∼8.3%) have |β| < 20. The dis-

tribution in ecliptic latitude (Fig. 6) is distinctly broader than provided by Chesley & Spahr

(2004) who showed cumulative detections made by a simulated version of the LINEAR sur-

vey (Stokes et al. 2000). The broad distribution in ecliptic latitude suggests that there is

merit in extending searches for PHOs in the sweet spots to ecliptic latitudes of ±20. Since

the southern parts of these extended sweet spots are close to the horizon from the northern

hemisphere, and the northern parts of the extended sweet spots are close to the horizon from

the southern hemisphere, this in turn suggests that there is merit in conducting searches for

PHOs from both hemispheres or from space (e.g. Hildebrand et al. 2007).

The middle and bottom distributions in Fig. 5 show the location of the same sample

of objects 20 years before impact but with brighter magnitude limits of V < 20.7 and

V < 18.7. Another way to interpret these figures is that they show the detectability (for

the same limiting magnitude of V < 22.7) of H = 22 (diameter 140 m) and H = 24 (55 m)

impactors at this particular time. The smaller objects must be closer to the Earth in order

to be above the system’s limiting magnitude but this also has the effect of increasing the

phase angle which further decreases the apparent magnitude. Thus, smaller objects must

be closer and have smaller phase angle to be detected. While searches for larger objects

are efficient in the sweet spots they should be supplemented by opposition surveys to find

smaller objects. e.g. 20 years before impact 2008 TC3 had an apparent magnitude of V ≈ 31

with an ecliptic opposition-centered longitude of λopp ≈ −92 and latitude of β ≈ 2 — not

detectable but in the sweet spot region.

Figures 7a-d show the development of the sky-plane distribution of impactors as a

7Although Figure 5a shows the sky-plane distribution of Earth-impacting asteroids 20 years before impact

we have verified that the distribution is the same for earlier pre-impact times.

– 10 –

function of time before impact.

• 1 day before impact the impactors are located in two main concentrations; one centered

on the opposition direction and the other centered on the Sun. The impactors are

widely spread in ecliptic latitude because they are close to the Earth. About half

as many impactors approach from the λopp > 0 (a.m./morning) side compared to the

λopp < 0 (p.m./evening) side. Objects that approach from the morning side are moving

more slowly around the Sun than the Earth, meaning that the Earth runs into them.

They have perihelia that are well inside the Earth’s orbit, or have higher inclinations.

Objects that impact on the evening side catch up with the Earth in its orbit around

the Sun. They have perihelia that are closer to the Earth’s orbit, or have higher

eccentricities.

• 30 days before impact, the concentration that will impact from the opposition direction

has moved east and is centered close to λopp = 20. The impactors that will approach

from close to the Sun direction are also further east with some of them becoming

observable in the evening sweet spot.

• 60 days before impact many of the impactors that will approach the Earth from outside

the Earth’s orbit are scattered around λopp = 40 and more of the impactors that will

approach from inside the Earth’s orbit are becoming visible near the evening sweet spot.

This trend continues 90 days and 120 days before impact with the outside impactors

moving further east and more of the inside impactors becoming more visible in the

evening sweet spot.

• More than 180 days before impact the sky plane distribution of the impactors is more

complex. The observability of impactors decreases significantly because of their small

solar elongations. 180 days, 1 year and 1.5 years before impact many impactors are

close to the direction of the Sun or are far from the Earth. Observability improves from

2 years onwards as the distribution more closely mimics the steady state distribution

of impactors in the sky.

The difficulty in observing many of the impactors in the period between 0.5 and 1.5

years before collision with the Earth is important. In the event that an impact is predicted,

precision astrometry will be needed during this period to determine where and when the

impact will occur so that life-saving actions can be taken if necessary.

– 11 –

3. Next generation sky survey impactor detection performance

Our goals in this section are to determine

• the efficiency of a next-generation sky survey at identifying Earth-impacting asteroids

• the likely warning time for impending impacts

• the reason(s) why some impactors remain undetected

• methods for discovering the impactors that are most difficult to detect

• the probability that a next-generation survey will identify an impacting object as a

function of its diameter

There have been numerous efforts in the recent past to simulate the performance of indi-

vidual ground and/or space-based sky surveys at detecting NEOs (e.g. Bowell & Muinonen

1994; Jedicke et al. 2003; Harris & Bowell, 2004; Stokes et al. 2004; Ivezic et al. 2007;

Moon et al. 2008) but only Chesley & Spahr (2004) concentrated specifically on identifying

impactors and their work also simulated the performance of the last generation of asteroid

surveys. As discussed above, the impactors have a different orbit distribution from the NEO

or even PHO population and pose different challenges to a survey and its moving object

detection system. These include some pathological cases in the distribution of synodic peri-

ods for the objects, the fact that they are infrequently close enough and above the limiting

magnitude of the detection system, and that at small topocentric distance their apparent

rate of motion on the sky can be very small (mimicking more distant objects) and rapidly

varying due to the topocentric motion of the observer. For all these reasons, when simulating

the detection of impactors it is probably not sufficient to assume that all the objects will be

detected and identified as imminently hazardous. A high-fidelity simulation is required that

models the entire detection process from imaging through orbit determination and hazard

assessment.

The Pan-STARRS surveying mode has not yet been decided upon and, realistically, will

asymptotically approach its final configuration during the first year of operation. On average,

each month PS1 will survey π/2 steradians or ∼5,000 square degrees in an ‘opposition’ survey

with an overlap between months of about π/4 steradians. The opposition fields are imaged

in g, r, and i each lunation near new moon. The redder (z, y) filter observations are obtained

near quadrature closer to full moon to take advantage of their reduced sensitivity to scattered

moonlight. Each field will be imaged twice (15-30 minutes apart) in each filter in each month

and imaged in two lunations/year due to the overlapping survey area from month to month.

– 12 –

We employed the Pan-STARRS Moving Object Processing System (MOPS) to process

synthetic detections generated in a pseudo-realistic Pan-STARRS survey. The simulated

survey covers a large region (3600 deg2) of the sky around opposition (within roughly ±30

from opposition in longitude and ±30 from the ecliptic) and two ∼ 600 deg2 regions in the

sweet spots defined by Chesley & Spahr (2004) within ±10 of the ecliptic and from about

60 to 90 solar elongation. It is essentially a solar system specific sub-set of the sky that

the Pan-STARRS system is expected to cover when it becomes operational.

The survey simulator is described in detail in Jedicke et al. (2005) and Denneau et al.

(2007). It incorporates a crude weather simulation and a realistic survey pattern that at-

tempts to observe fields at high altitude and on the meridian. We use a full N-body ephemeris

determination to calculate the exact (RA,Dec) of each impactor in each synthetic field and

then add noise to the astrometric position according to the expected PS1 S/N-dependent

astrometric error model. The photometry for each object is similarly degraded and then we

make a cut at S/N=5 in order to simulate the statistical loss of detections near the system’s

limiting magnitude (V = 22.7). Each field is observed twice each night within ∼15 minutes

to allow the formation of ‘tracklets’ — pairs of detections at nearly the same spatial location

that might represent the same solar system object. Fields are re-observed 3 times per luna-

tion (weather permitting) and tracklets are linked across nights to form ‘tracks’ that are then

tested for consistency using an initial orbit determination (IOD). Detections in tracks with

small astrometric residuals in the IOD are subsequently differentially corrected to obtain a

final orbit. The major item that is not simulated is the effect of the camera fill-factor and

this could have a major impact on the survey’s efficiency. We will estimate this effect below

but the simulation is otherwise one of the highest fidelity moving object simulations ever

attempted.

We anticipate that there may be concerns regarding simulating the performance of

detector systems especially in the sense that the simulations tend to be optimistic compared

to the actual detector. In particular, in this case we have

1. used a realistic survey scenario but it is not the survey that will eventually be imple-

mented by PS1,

2. used a simplistic weather model,

3. used a S/N-dependent astrometric error that is more appropriate to future surveys

with better catalogs (at the onset of operations PS1 will probably use the USNO-B

catalog (Monet et al. 2003) which will limit absolute astrometry to worse than 0.1′′),

4. not incorporated false detections,

– 13 –

5. used an early version of the MOPS with reduced efficiency compared to the most recent

version (∼80% vs. ∼100%),

6. not accounted for the camera fill-factor (the fraction of ‘live’ pixels on the detector

compared to the footprint of the focal plane on the sky).

We think that the first three factors are relatively unimportant. The implemented

survey scenario is quite good and surveys most of the sky in which solar system objects will

appear. The weather model is simple but has the desired effect of disrupting the cadence

of observations and sometimes eliminating lunations from consideration due to there being

too many bad nights. We have also tested MOPS performance under conditions of larger

astrometric uncertainty and find that it still performs well.

The fact that no false detections were used in the simulation is also unimportant. In

targetted smaller simulations (e.g. Milani et al. 2008) we tested the MOPS using a full

density complement of false and synthetic asteroid detections and found no degradation in

performance at the 5-σ level. In those tests the minimum ratio of false:synthetic detections

was 1:1 on the ecliptic where the density of synthetic asteroid detections is highest. Since

the density of asteroids decreases rapidly with latitude the false:synthetic ratio increases dra-

matically toward the ecliptic poles. Still, few tracklets incorporate false detections because

those detections are spatially uncorrelated (in the simulation). It is likely that real survey

systems will produce correlated false detections near chip gaps, due to CCD defects, diffrac-

tion spikes, etc., and this will produce more false tracklets than our simulation. However,

the false tracklets will not link to other tracklets on other days and, if they do, will not pass

quality control checks on the derived orbit. Furthermore, MOPS makes use of the detection’s

morphology when combining detections into tracklets - the distance between the detections

must be consistent with trailing observed in the detections themselves. Indeed, we have

employed MOPS to identify asteroids in real data from the CFHT telescope (Masiero et al.

2009) and from Spacewatch (e.g. Larsen et al. 2007) with excellent performance.

The last two factors are most important. The reduced efficiency of the MOPS software

used in this simulation will have a proportional effect on the number of simulated impactor

discoveries - about a 20% reduction. The actual system performance will therefore be about

25% better than reported here.

On the other hand, the largest negative impact on the simulation will be the PS1 camera

fill-factor. The effective camera fill-factor (f) is reduced by the metal lines between individual

OTA cells, the gaps between the CCDs, the use of some cells for guide star acquisition,

dead cells, bad cells (e.g. due to charge transfer efficiency problems or dark noise) and the

removal of portions of the image by the PS1 funding agency to excise fast moving satellites.

– 14 –

We expect the overall fill-factor due to all these effects to result in f ∼ 0.88. As described

above, for solar system discoveries we require 6 detections on 3 nights within a lunation.

Thus, the impact of the fill-factor on the detection efficiency (ǫ) for fast moving objects like

the impactor population is simply ǫ = f 6 ∼ 0.46 if the inactive area is uncorrelated on the

focal plane or ǫ = f 3 ∼ 0.68 if it is correlated. That is, if the first detection of an object

appears on an inactive area then its second detection is also likely to appear on an inactive

area in the ‘correlated’ case and unlikely to do so in the ‘uncorrelated’ case. Losing 1

3to 1

2

of potential discoveries due to the fill-factor is unfortunate but the loss is mitigated for slow

moving distant objects because they appear near opposition in successive lunations. PS1 has

two opportunities to discover the object in each of two successive lunations so the efficiency

for finding these objects will be & 90%. The problem is worse for objects like NEOs and

impactors that spend fewer lunations above the detection threshold.

To determine the Pan-STARRS (PS1) survey efficiency for detecting impacting asteroids

as a function of time and size we divided our sample of ∼130,000 synthetic impactors into

six independent sets that were assigned different absolute magnitudes (H) as shown in Table

2. We can assign any H to the impactors because the Bottke NEO model assumed that the

size distribution of the NEOs was independent of the orbital elements. The six selected sizes

span almost two orders of magnitude in diameter. The number of objects of each size was

selected to provide a good number of derived objects (after processing through MOPS) and

yet not so many objects as to be prohibitively expensive in processing time. Each of these

six independent sets of impactors were then run through a simulation of the PS1+MOPS

system.

Figure 8 shows that the efficiency of the PS1 survey at detecting impactors increases

as a function of time and impactor diameter. In just four years of PS1 operations it could

identify ∼85% of all 1 km diameter objects that will impact the Earth in the next 100

years. Interestingly, it has a ∼74% chance of identifying a 1 km diameter that would impact

during the 4 year time span of the survey. At first glance this is surprising since PS1 can

detect a 1 km diameter asteroid at opposition at a geocentric distance of ∼2.67 AU. The

objects should be visible long before impact in the large volume of space surveyed by the

PS1 system. We will explore the reasons for the ineffectiveness of the survey at detecting

these large hazardous objects below.

The impactor discovery efficiency increases nearly linearly with time for objects of 200 m

diameter to ∼40% efficiency in just four years. While this behavior cannot increase indef-

initely we estimate that after 12 years the efficiency may be ∼80%. This is an interesting

– 15 –

value because the Pan-STARRS PS4 system will have 4× the collecting area8 of the PS1

system modelled here and thus the efficiency curve for 200 m diameter objects for PS1 corre-

sponds to the 100 m diameter efficiency curve for PS4. Thus, during its anticipated 10 year

survey mission PS4 alone may reach nearly 90% completion for objects ≥140 m diameter or

larger that will impact in the next 100 years.

Table 2: Size frequency distribution of synthetic impactors used in the PS1 survey simulation.

The conversion between diameter and absolute magnitude assumes an albedo of p = 0.14 for

NEOs (Stuart & Binzel 2004).

diameter absolute number

(meters) magnitude

1000 17.75 1193

500 19.25 3816

200 21.25 4804

100 22.75 10001

50 24.25 25001

20 26.25 85000

Total 129815

The impact warning time was defined by Chodas & Giorgini (2008) as the time between

impact and when the probability of an impact on the Earth is calculated to be more than

50%. However, we believe that the experience and response to the discovery of (99942)

Apophis shows that the impact awareness time for an object is considerably longer than

the impact warning time. Once an object is discovered that has a non-zero probability of

impact it is observed obsessively at every opportunity and impact calculations are regularly

refined to monitor the impact probability. We define the impact awareness time as the

period between the identification of an impactor as a PHO (MOID < 0.05 AU) and its time

of impact. As discussed above, almost all the impactors in this study have MOID ≪ 0.05 AU

long before impact.

Fig. 9 (top) shows the MOID for derived objects at discovery (when at least 3 nights

of observations have been obtained in the course of a single lunation). Almost all the

objects will immediately be flagged as PHOs and therefore start the impact awareness time

clock. The error on the MOIDs, the difference between the MOID for the synthetic object

8Since the PS4 system employs 4 separate cameras viewing the same field the PS4 image stacks will have

∼100% fill-factor.

– 16 –

and the MOID for the derived object, are small after just a single lunation with typical

∆MOID∼MOID∼ 10−3 AU. As more observations are acquired for these objects the impact

probability should monotonically increase to 100%.

Figure 10 shows the impact awareness time as a function of the impactor size. Since

the synthetic impactors were designed to hit the Earth at random times over the next 100

years, and large objects can be detected long before impact, it is no surprise that the impact

awareness time for large discovered synthetic objects is evenly distributed over 100 years

(Figure 10 top). The apparent decrease in the fraction of 1000 m objects with larger impact

awareness times is an artifact of statistics - fitting a line to the distribution shows that it is

consistent with being flat at the 1-σ level. Surprisingly, the impact awareness times for small

discovered synthetic objects is also evenly distributed over 100 years (Figure 10 bottom).

This is because when PS1 discovers an object and observes it on ≥3 nights over an ∼ 10 day

period the orbit is good enough to accurately determine the MOID and determine the impact

awareness time. Of course, it may be difficult to obtain followup observations of the smallest

objects to refine the orbit and the impact probability calculation.

It is important to keep in mind that Fig. 10 does not include the large spike at zero

warning time due to the undiscovered objects. For example, Figure 8 shows that ∼60% of

200 m diameter objects remain undiscovered at the end of the four years of PS1 surveying.

Thus, the most probable awareness (warning) time for the smaller objects is zero. But when

they are discovered before the apparition in which they impact the warning time can be many

decades. As discussed above, to be 90% effective at eliminating the risk of an unanticipated

impact in the next 100 years for objects >140 m diameter requires a PS1-like system to

survey much longer or a more powerful system like PS4 (Kaiser & the Pan-STARRS Team

2005) or the system being developed by the LSSTC (Ivezic et al. 2007).

While it is interesting to compute the efficiency with which a next generation survey

such as PS1 can find impacting asteroids the reality of the situation is that it is unlikely

that any large objects are on a collision course with the Earth in the next 100 years. The

expected number of detected impactors, N(D), is simply the product of the efficiency, ǫ(D),

for detecting impactors of diameter D and the size-frequency distribution of the population,

n(D). The efficiency was already shown in Fig. 8 forD > 20 m. We use Brown et al. (2002)’s

determination of the annual cumulative number of objects striking the Earth’s atmosphere:

N(> D) = 37(D/meters)−2.7 which implies that objects in the size range of 2008 TC3 strike

the Earth about twice per year. Fig. 11 shows that unless the Earth is extremely unlucky PS1

will not detect a large (D > 20 m) impacting asteroid. A best case linear extrapolation of

ǫ(D) to D < 20 m using just the 20 m and 50 m diameter points suggests that the likelihood

of obtaining 3 nights of detections in the discovery of even smaller impactors is extremely

– 17 –

unlikely. The efficiency is decreasing faster with smaller diameter than the number of objects

is increasing.

While it is unlikely that PS1 will single-handedly obtain enough detections to determine

a pre-impact orbit, the possibility of detecting a small asteroid prior to impact (such as the

impactor 2008 TC3), or precovering the asteroid after impact using an orbit derived from the

bolide trajectory, is also interesting to meteoriticists. With sufficient advance notice it would

be possible to organize a ground-based team to observe the asteroid’s atmospheric entry, train

space-based platforms on the impact location, and prepare for recovery of meteorites. Post-

impact precovery of the object could be useful to help determine the pre-impact size of the

object and to verify the pre-impact orbit determination for the bolides (e.g. Abe 2008).

Simulating the automated detection by PS1+MOPS of smaller impactors is difficult.

At the current time MOPS operates by linking together tracklets on 3 nights taken over the

course of ∼ 10 days. With typical impact velocities of ∼ 15 km/s the best case scenario

requires that PS1+MOPS first detect the object at a distance of ∼ 13 × 106 km (approx-

imately 10 days before impact). At PS1’s assumed limiting magnitude of V = 22.7 this

requires that the object be > 3m in diameter. Even if this situation were to unfold, varia-

tions in the object’s apparent position and velocity on the sky due to the topocentric motion

of the observatory would likely render the object difficult to link within the MOPS (though

we have not yet studied this scenario in detail). Instead, we consider the possibility that

PS1 will detect an impacting asteroid prior to impact but on too few nights to determine a

pre-impact orbit.

It is unlikely that the smallest objects (< 20 m diameter) will be discovered, and have

good enough derived orbits to guarantee impact, in any apparition except for the one in

which they strike the Earth. Thus, we determined the sky-plane distribution and rate of

motion 1, 5 and 10 days before impact for all the objects in Table 2.

Once again, since the Bottke NEO model’s orbit distribution is independent of size, and

assuming that we can extend the orbit distribution of the large objects down to 1 m diameter

(we have already discussed that while there is reason to believe that the Yarkovsky effect will

modify the orbit distribution there is as of yet no debiased orbit distribution for the small

impactors), we can assign any size or H to the objects and quickly determine the ensemble’s

apparent magnitude distribution. The efficiency for detecting these objects is then simply

the ratio between the number that meet all our search criteria (within the surveying region,

V < 22.7, assuming that surveying takes place on only 75% of nights due to weather, and

with a rate of motion within the detectability range) and the total number. Fig. 12 shows

that the maximum efficiency for the smallest objects is about 0.6%.

– 18 –

The distributions of the rates of motion of the meteoroids before impact are shown in

Fig. 13. Typical rates of motion are much slower on the final approach trajectory than on

fly-by apparitions. The detectable rates of motion are limited to 0 ≤ ω ≤ 12 deg/day where

the upper limit is enforced by the Pan-STARRS funding agency. The figure shows clearly

that the restricted rate of motion does not have a strong effect on detection efficiency when

the impactors are on their approach to the Earth.

In the discussion above and elsewhere in this work we have ignored the effects of trailing

loss — when objects move during the exposure time they leave ‘trails’ on the image rather

than point sources and the trails have, in the past, been more difficult to identify than point

sources. While the PS1 point source detection limit is expected to be V ∼ 22.7 the efficiency

of our faint trail detection algorithm is not yet known. It is thought that it should be efficient

to per-pixel S/N ≪ 1 implying that the detection efficiency could be quite good even for

intrinsically faint objects. Since we have not yet measured the trailing losses we ignore them.

This means that the small impactor detection efficiencies reported here and in Fig. 12 are

upper limits.

Figure 11 shows the expected number of detections of small impactors (bolides) within 10

days of impact during the 4 year PS1 survey as a function of diameter using the Brown et al.

(2002) size-frequency distribution (SFD). The cumulative probability of PS1 detecting a

bolide in the 1-10 m size range is 25± 15% (the error is determined from the SFD only). In

other words, PS1 has ∼ 25% probability of detecting another 2008 TC3-like object during

its four year survey mission.

Considering that we have argued that PS1 is the first of the next generation sky-surveys

and that this powerful system only has a ∼ 25% probability of detecting another 2008 TC3-

like object in four surveying years, how could a ‘last-generation’ survey like CSS have dis-

covered 2008 TC3? In addition to the impactor, the CSS has also discovered several other

small asteroids making very close approaches to the Earth (e.g. 2008 UA202). The CSS’s

telescope system has (Ed Beshore, personal communication) a smaller etendue (1.5 m × 1

deg2) than the PS1 system (1.8 m × 7 deg2) at a significantly worse site (CSS FWHM ∼ 2′′

vs ∼ 1′′ for PS1; worse weather conditions; brighter sky), and twice the camera readout time

(∼ 12 s vs. ∼ 6s). Thus, we conservatively estimate that the PS1 system will be ∼ 10× more

efficient than the CSS. The CSS survey strategy sacrifices limiting magnitude to cover as

much sky as possible (T. Spahr, personal communication) — an old recipe for finding more

NEOs (Bowell & Muinonen 1994). The result is that the CSS 1.5 m telescope covers about

3600 deg2 per lunation to V ∼ 21 mag while our PS1 simulation covers ∼3800 deg2 to a

limiting magnitude of V ∼ 22.7. Based on these arguments our simulations suggest that the

CSS made a low-probability discovery of 2008 TC3 — they were lucky. Another alternative

– 19 –

is that the SFD of the bolides from Brown et al. (2002) is in error — we consider this to be

unlikely because of other corroborating research (e.g. Ivanov 2006).

Like the CSS discovery of 2008 TC3, the problem is that PS1 will detect the object

on only a single night resulting in an orbit with large uncertainties. PS1 can report single

night detection pairs to the Minor Planet Center (MPC) but will then depend on rapid

announcement by the MPC of likely impactors and prompt followup by other observatories

around the world.

We have considered the possibility that detections in the impactor’s tracklet could pro-

vide information to flag it as an imminent impactor based on rapid changes in the detections’

trail length or orientation due to the effects of topocentric parallax. While the 15-30 min

time difference between the detections in the tracklets probably does not provide enough

leverage to make this method viable for Pan-STARRS it could be employed in the future by

a dedicated impactor survey.

Since ground-based all-sky bolide impact monitoring networks (e.g. Oberst 1998; Weryk

2008; Bland 2008) cover an extremely small fraction of the Earth’s surface (∼1%; P. Brown,

personal communication) it is exceedingly unlikely that an object imaged by PS1 will also

be detected by a ground-based sensor. On the other hand, the detection of bolides from

wide-coverage space-based systems (e.g. Koschny et al. 2004) is possible and may provide

an opportunity to search through PS1 detections for pre-impact observations.

Figure 14 shows the apparent sky-plane distribution for 3 m diameter bolides 1 day

before impact. These small objects (e.g. 1-20 m) are visible for only a short time before

impact and their apparent brightness is strongly affected by the phase angle so that they can

only be detected near opposition. The location of 2008 TC3 3 days before impact is clearly

within the PS1 opposition field. PS1 would have detected 2008 TC3 since it was brighter

than V=22.7 mag (assuming H = 30.4 and G = 0.15) for 4–5 days before impact (with

V = 18.9 mag at discovery 1 day before the impact) and the sky-plane motion was below

the PS1 trailing cut-off of 12/day.

Although the small impactors may be located over the entire sky there are two promi-

nent clumps in Fig. 14 — towards the Sun and around the opposition point (the anti-solar

direction). This result is consistent with the helion and antihelion sources (Poole 1997) of

sporadic background bolides that are the result of the velocity vector summation of the

Earth and the sporadic meteors. Jones & Brown (1993) had earlier suggested that these

two sources of sporadic meteors were most consistent with a population of small meteoroids

derived from a Jupiter Family Comet (JFC) parent population. We note that their study did

not correct for strong selection effects in the radar detection of the meteors that would favor

– 20 –

the high velocity cometary sub-component of the helion and anti-helion sources. Considering

that the Bottke NEO model employed here is dominated by asteroids but still produces these

two sources it suggests that at least some component of the sporadic meteors in the helion

and anti-helion regions may be of asteroidal origin.

We believe that our results encourage optimism that the suite of next generation ground-

based sky surveys will be able to eliminate ≥90% of the risk of an unanticipated impact of

an object > 140 m diameter. Still, it is interesting to identify a survey strategy that could

reduce the risk even further. Figure 15 shows that the undiscovered large (1 km) impactors

rarely appear in the PS1 survey regions and are strongly clustered in the direction towards

the Sun. This is not because the objects are on orbits interior to the Earth’s orbit (e.g.

Zavodny et al. 2008) but is due to their orbital period being close to one year. The synodic

period with respect to Earth Psyn = |P−1

Earth − P−1

asteroid|−1 is thus long. The four year PS1

survey has a low efficiency for detecting objects with long synodic periods and the solution

is to survey over a longer time period or to survey the sky at smaller solar elongations. The

suite of next generation surveys (e.g. , Pan-STARRS, LSSTC) will survey the sky for about

a decade and will increase the completion statistics at all impactor sizes. Surveying closer

to the Sun is realistic only from future space-based platforms (e.g. Tedesco et al. 2000;

Jedicke et al. 2003; Hildebrand et al. 2007; Mottola 2008).

Figure 16 shows the orbital period for 1 km diameter impactors that strike the Earth

during the 4 year survey mission. The orbital period of the undetected impactors peaks at 1

year as explained above. At first glance it may be surprising that a powerful survey system

could miss these large impactors given the large distance at which 1 km diameter objects

can be detected. The explanation is that all the undetected large impactors strike the Earth

in the first 2 years; before the survey had sufficient time to explore the entire volume of the

solar system to the distance at which 1 km diameter objects are detectable.

4. Conclusions/Discussion

We have used a synthetic population of Earth-impacting asteroids to determine their

sky-plane distribution and detectability with one of the next generation all-sky surveys, PS1.

We find that

• while the steady state sky plane distribution of the impactors is concentrated towards

small solar elongation as shown by Chesley & Spahr (2004) their sky-plane distribution

exhibits interesting behavior in the couple years leading up to impact. This behavior

could be exploited to identify these objects well in advance of impact.

– 21 –

• the requirement that a PHO have a MOID<0.05 AU identifies 98% of all impactors

even 100 years in advance of impact. The remaining 2% have much larger MOID and

the error on the MOID will not identify these objects as potential impactors since

they become PHOs only after encounter with another solar system object, usually

Jupiter. However, numerical exploration of their orbit evolution as routinely performed

by impact monitoring sites will generally reveal these hazardous objects long before

impact.

• the MOIDs determined for objects with detections obtained during just a single luna-

tion are very good

• the impactor model that we have developed is probably a good proxy for the unbi-

ased orbit distribution of the large bolide population based on 1) the good agreement

between the impactor orbit distribution and the orbit elements for impacting asteroid

2008 TC3 and 2) its sky-plane location at the time of discovery.

• the next generation of all-sky surveys will identify a large fraction (& 90%) of impactors

>140 m diameter in a decade-long survey designed to find them.

• the impact awareness time before impact can be many decades for impactors of any

size as long as they are discovered before impact. The most likely impact awareness

time for smaller impactors is zero.

• the next generation surveys will probably image a small impactor before impact but

it will likely be observed over too short a time span (e.g. one night) to allow either an

accurate pre-impact orbit to be computed or its identification as an imminent impactor.

• a search for pre-impact detections of a bolide is possible

• the most difficult objects to discover are those with long synodic periods relative to

the Earth.

• next generation surveys like PS1 will be efficient at detecting large impactors when

their impact time is more than about 2 years after the start of the survey.

– 22 –

Acknowledgements

This work was performed in collaboration with Spacewatch, LSSTC, CMU’s AUTON

lab, and the AstDyS team (Andrea Milani, Giovanni Gronchi and Zoran Knezevic). Steve

Chesley’s work was conducted at the Jet Propulsion Laboratory, California Institute of

Technology, under a contract with the National Aeronautics and Space Administration. The

design and construction of the Panoramic Survey Telescope and Rapid Response System

by the University of Hawaii Institute for Astronomy is funded by the United States Air

Force Research Laboratory (AFRL, Albuquerque, NM) through grant number F29601-02-

1-0268. MOPS is also supported by a grant (NNX07AL28G) to Robert Jedicke from the

NASA NEOO program. Andrea Milani, Giovanni Gronchi and Zoran Knezevic of the Ast-

DyS group provided critical orbit determination software to the MOPS team. The MOPS

is currently being developed in association with the Large Synoptic Survey Telescope Cor-

poration (LSSTC). The LSSTC’s research and development effort is funded in part by the

National Science Foundation under Scientific Program Order No. 9 (AST-0551161) through

Cooperative Agreement AST-0132798. Additional funding to the LSSTC comes from private

donations, in-kind support at Department of Energy laboratories and other LSSTC Institu-

tional Members. Veres was supported by the National Scholarship Programme of the Slovak

Republic, the European Social Fund, a Grant from Comenius University (No. UK/399/2008)

and VEGA Grant No. 1/3067/06.

– 23 –

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This preprint was prepared with the AAS LATEX macros v5.2.

– 29 –

0 40 80 120 1600.00

0.05

0.10

0.15

0.20

0.0 0.2 0.4 0.6 0.8 1.00.00

0.02

0.04

0.06

0.08

0.10

0.12

0 1 2 3 4 50.00

0.02

0.04

0.06

0.08

0.10

2008 TC3 impactors sporadic background fireballs NEO model

Frac

tion

Inclination

2008 TC3 impactors sporadic background fireballs NEO model

Frac

tion

Eccentricity

impactors sporadic background fireballs NEO model

Fr

actio

n

Semimajor Axis (AU)

2008 TC3

Fig. 1.— Semi-major axis (top), eccentricity (middle) and inclination (bottom) distribution

for (solid) our synthetic impactor population, (dotted) sporadic background fireballs and

(dashed) the Bottke NEO model. The semi-major axis distribution is not shown beyond

5.1 AU but these data are included in the eccentricity and inclination distributions. The

corresponding orbital elements for 2008 TC3 are indicated by the solid vertical line in each

figure.

– 30 –

1E-7 1E-6 1E-5 1E-4 1E-3 0,01 0,1 1m

ax E

CR

mo

de

EC

R

min

EC

R

Fra

ctio

n

MOID (AU)

orbital epochs

100 years

50 years

10 years

1 year

before impact

1

0.1

0.01

1E-3

1E-4

1E-7 1E-6 1E-5 1E-4 1E-3 0,01 0,1 1

ma

x E

CR

mo

de

EC

R

Fra

ctio

n

MOID (AU)

orbital epochs

30 days

10 days

5 days

1 days

before impact

1

0.1

0.01

1E-3

1E-4

min

EC

R

Fig. 2.— Fractional differential (solid) and cumulative (dashed) distribution of MOID for

synthetic impactors at different times before impact. The Earth capture radius (ECR) is

calculated for the highest (max ECR), most probable (mode ECR) and lowest (min ECR)

impactor encounter velocity. The bin size is log(MOID/AU) = 0.07 in both figures.

– 31 –

1 10 100 1000 10000

0.0

0.5

1.0

1.5

2.0

P

HO

Pro

babi

lity

Failu

re (%

)

Time Before the Impact (days)

Fig. 3.— The probability that an Earth-impacting asteroid will not be identified as a PHO

(MOID> 0.05AU) as a function of time before impact. The superimposed line is a fit

(R2 = 0.99) to an empirically defined function: p = 1.3× 10−4 + t0.92.

– 32 –

0.1 1 10 100 1000 100001E-3

0.01

0.1

1

10

MO

ID =

10-4

AU

Inte

rcep

t

Time Before the Impact (days)

1 10 100 1000 10000

1E-5

1E-4

1E-3

min ECR

mode ECR

Mo

st P

rob

ab

le M

OID

(A

U)

Time Before the Impact (days)

max ECR

Fig. 4.— (top) The constant (f ′) in a fit (log f = log f ′ + m log[MOID/(10−4AU)] with

f < 0.9) to the cumulative fraction (f) of impactors with MOID as a function of time before

impact from Figure 2. i.e. f ′ is the cumulative fraction of objects with MOID≤ 10−4 AU

at each of the specified time steps. The superimposed solid line is a fit (R2 = 0.954) to

an empirically defined function: log f ′ = a[log2(t/days) − log2(t0/days)] with t being the

time before impact, a = −0.079 and t0 = 72.8 days. (bottom) The most probable MOID

(mode) for the impactors as a function of time before impact. The superimposed solid

line is a fit (R2 = 0.90) to an empirically defined function: MOID (AU)= −0.014 − 1.5 ×

10−3 ln [((t/days) + 105)]. The Earth capture radius is shown for the highest (max ECR),

most probable (mode ECR) and lowest (min ECR) encounter velocity for the impactors.

– 33 –

-50

0

50

100 0 -100

-50

0

50

100 0 -100

-50

0

50

Eclip

tic L

atitu

de

Opposition Centered Ecliptic Longitude

Fig. 5.— Topocentric opposition centered ecliptic sky plane distribution of H = 20 (∼350 m

diameter) Earth-impacting asteroids 20 years before impact for a survey with a limiting

magnitude of (top) V = 22.7 (middle) V = 20.7 and (bottom) V = 18.7. This is sufficiently

in advance of impact to represent the impactors’s steady-state sky plane distribution.

– 34 –

-50 0 50

0.00

0.05

0.10

0.15

Frac

tion

Ecliptic Latitude

Fig. 6.— Ecliptic latitude distribution of Earth-impacting asteroids with V < 22.7 twenty

years before impact.

– 35 –

-50

0

50

100 0 -100

-50

0

50

100 0 -100

-50

0

50

Eclip

tic L

atitu

de

Opposition Centered Ecliptic Longitude

Fig. 7.— a) Topocentric opposition centered ecliptic sky plane distribution of Earth-

impacting asteroids with V ≤ 22.7 (top) 1 day, (middle) 30 days, and (bottom) 60 days

before impact.

– 36 –

-50

0

50

100 0 -100

-50

0

50

100 0 -100

-50

0

50

Eclip

tic L

atitu

de

Opposition Centered Ecliptic Longitude

Fig. 7.— b) The opposition centered ecliptic sky plane distribution of Earth-impacting

asteroids with V ≤ 22.7 (top) 90 days, (middle) 120 days, and (bottom) 150 days before

impact.

– 37 –

-50

0

50

100 0 -100

-50

0

50

100 0 -100

-50

0

50

Eclip

tic L

atitu

de

Opposition Centered Ecliptic Longitude

Fig. 7.— c) The opposition centered ecliptic sky plane distribution of Earth-impacting

asteroids with V ≤ 22.7 (top) 180 days, (middle) 1 year, and (bottom) 1.5 years before

impact.

– 38 –

100 0 -100

-50

0

50

E

clip

tic L

atitu

de

Opposition Centered Ecliptic Longitude

Fig. 7.— d) The opposition centered ecliptic sky plane distribution of Earth-impacting

asteroids with V ≤ 22.7 2 years before impact.

– 39 –

1 10 100 10001E-5

1E-4

1E-3

0.01

0.1

1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0.0

0.2

0.4

0.6

0.8

1.0

Impactor Diameter (m)

7%26%

Co

mp

lete

ne

ss

Co

mp

lete

ne

ss

Survey Time (Years)

impactor diameter 1000m 500m 200m 100m 50m 20m

74%

43%

65%

0.3%

Fig. 8.— (left) PS1 survey completeness (efficiency) as a function of time for different size

impactors assuming an albedo of 0.14. The percentages on the right side of the figure adjacent

to the efficiency curves are the efficiency for detecting an impactor that strikes the Earth

during the 4 year survey. (right) The efficiency for discovering objects impacting during the

4 year survey as a function of impactor diameter. A linear extrapolation to D < 20 m using

the two leftmost data points is shown with a dashed line.

– 40 –

1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.11E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

0.025

0.050

0.075

0.025 0.050 0.075

|| M

OID

(AU

)

Derived MOID (AU) Fraction

Fra

ctio

n

Fig. 9.— (lower-left) The distribution of the error in the MOID

(|MOIDsynthetic−MOIDderived|) vs. the derived MOID for impactors detected in the

simulation. (right) Distribution of the error in the MOID. (top) Distribution of the derived

MOID.

– 41 –

0 20 40 60 80 1000.00

0.05

0.10

0.15

Frac

tion

Impact Awareness Time (years)

impactor diameter 1000m 500m 200m

0 20 40 60 80 1000.00

0.05

0.10

0.15

Frac

tion

Impact Awareness Time (years)

impactor diameter 100m 50m 20m

Fig. 10.— Distribution of impact awareness times (defined in the text) for discovered syn-

thetic impactors of different sizes. Note that the awareness time is zero for undiscovered

impactors and they are not included in this figure.

– 42 –

1 10 100 10001E-5

1E-4

1E-3

0.01

0.1

1

future impacts instant impacts

Impactor Diameter (m)

Num

ber o

f Disc

over

ed Im

pact

ors

2008

TC3

Fig. 11.— (solid) Expected number of detections of large (> 20 m diameter) impactors that

will strike the Earth in the next 100 years that are observed 3 nights in a single lunation

during a four year PS1 survey and (dashed) the number of small (1-20 m diameter) impactors

detected by the PS1 system in the lunation prior to impact. The probable size range of the

impacting asteroid 2008 TC3 is indicated by the shaded region.

– 43 –

1 10 1001E-4

1E-3

0.01

0.1 1day 5days 10days

before the impact

C

ompl

eten

ess

Diameter (m)

Fig. 12.— Estimated four year PS1 survey detection efficiency 1, 5, and 10 days before

impact for small impactors on their final approach to the Earth.

– 44 –

1E-3 0.01 0.1 1 100.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

Fr

actio

n

Apparent Motion (deg/day)

1 day 5 days 10 days

before the impact

Fig. 13.— Distributions of the apparent rate of motion for small impactors 1, 5, and 10

days before impact. There is no restriction on apparent magnitude. The upper limit on the

detectable rate of motion imposed by the Pan-STARRS funding agency is 12 deg/day.

– 45 –

-50

0

50

100 0 -100

-50

0

50

Opposition Centered Ecliptic Longitude

Ecl

iptic

Lat

itude

2008 TC3

Fig. 14.— (top) Sky-plane probability distribution for 3 m diameter impactors (bolides) 1

day before impact with no restrictions on brightness and apparent motion. (bottom) Same

as above but with V < 22.7 and apparent motion < 12 deg/day. Approximate PS1 search

regions are shown as solid rectangles (the opposition region is in the center and the sweet

spots are on the left and right). The position of 2008 TC3 at discovery by the Catalina Sky

Survey is highlighted.

– 46 –

-50

0

50

100 0 -100

-50

0

50

Opposition Centered Ecliptic Longitude

Ecl

iptic

Lat

itude

Fig. 15.— (top) Sky-plane position probability distribution for 1 km diameter impactors

that were not discovered during the simulated 4 year PS1 survey mission with no restriction

on the apparent magnitude. Darker regions represent where the objects are most likely to be

found. (bottom) Same as above but imposing a PS1 limiting magnitude cutoff at V = 22.7.

Approximate PS1 search regions are shown as solid rectangles.

– 47 –

1 2 3 40

20

40

60

80

1001km size population

undetected found

Num

ber

Orbital period (years)

Fig. 16.— Orbital period distribution for found (dotted) and undetected (solid) 1 km diam-

eter impactors during the 4 year PS1 survey mission.